find-the-domain-and-range-of-y-4x-2-3-x-lt-2-3x-1-x-2-

Question Number 5237 by sanusihammed last updated on 02/May/16

f i n d t h e d o m a i n a n d r a n g e o f

y = [_{4 x^{2} + 3 x < 2}^{3 x - 1 x ⩾ 2}

Answered by FilupSmith last updated on 02/May/16

D o m a i n = {x : - \infty ⩽ x ⩽ \infty}

{R a n g e}_{1} y = 3 x - 1

{y : [3 (2) - 1] ⩽ y ⩽ \infty}

{y : 5 ⩽ y ⩽ \infty}

{R a n g e}_{2} y = 4 x^{2} + 3

{y : - \infty ⩽ y < [4 {(2)}^{2} + 3]}

{y : - \infty ⩽ y < 19}

∴ R a n g e = {y : - \infty ⩽ y ⩽ \infty}

Answered by Rasheed Soomro last updated on 02/May/16

y = [_{4 x^{2} + 3 x < 2}^{3 x - 1 x ⩾ 2}

The function is defined for all real

numbers . Hence domain of function

is R .

^{∙} For x ⩾ 2

x ⩾ 2

\Rightarrow 3 x ⩾ 6

\Rightarrow 3 x - 1 ⩾ 5

\Rightarrow y ⩾ 5

^{∙} For x < 2

x < 2

\Rightarrow x^{2} < 4

\Rightarrow {4 x}^{2} < 16

\Rightarrow {4 x}^{2} + 3 < 19

\Rightarrow y < 19

So the range is {y ∣ y \in R \land 5 ⩽ y < 19}

Commented by Yozzii last updated on 02/May/16

y ⩾ 3 . D o a s k e t c h g r a p h f o r y t o s e e

t h i s .

Commented by FilupSmith last updated on 02/May/16

A h i m i s w r o t e t h e f i n a l p a r t!

Commented by Rasheed Soomro last updated on 06/May/16

From graph I understand now that the range is {y : y \in R, y ⩾ 3}

Credit goes to Yozzi .

I think that for determining range of

a function its minima and maxima should

be considered .

Commented by Rasheed Soomro last updated on 05/May/16

Commented by Yozzii last updated on 06/May/16

Y o u a l s o n e e d t o t h e n f i n d o u t w h e t h e r

t h o s e s t a t i o n a r y p o i n t s a r e g l o b a l

o r l o c a l f o r a l l r e a l x . I f t h e s e p o i n t s

a r e g l o b a l t h e n y o u w o u l d h a v e f o u n d

o n e e n d o f t h e i n t e r v a l f o r y .

Facebook Tweet Pin